Unlike scepticism, fallibilism does not imply the need to abandon our knowledge - we needn't have logically conclusive justifications for what we know. Rather, it is an admission that because empirical knowledge can be revised by further observation, any of the things we take as knowledge might possibly turn out to be false. Some fallibilists make an exception for things that are axiomatically true (such as mathematical and logical knowledge). Others remain fallibilists about these as well, on the basis that, even if these axiomatic systems are in a sense infallible, we are still capable of error when working with these systems. Moreover, according to Gödel's incompleteness theorems, to find a complete and consistent set of axioms for all of mathematics is impossible, That is, even mathematics has its own paradox like the Barber paradox. The theory that it was impossible to know a truth with certainty was the basis of the educational movement lead by people like John Dewey and was called the pragmatist movement.

Moral fallibilism is a specific subset of the broader epistemological fallibilism outlined above. In the debate between moral subjectivism and moral objectivism, moral fallibilism holds out a third plausible stance: that objectively true moral standards exist, but that they cannot be reliably or conclusively determined by humans. This avoids the problems associated with the flexibility of subjectivism by retaining the idea that morality is not a matter of mere opinion, whilst accounting for the conflict between differing objective moralities. Notable proponents of such views are Isaiah Berlin (value pluralism) and Bernard Williams (perspectivism).